Question

Produtos Notáveis:
A-) (x+3).(x+4)
B-) (a+1).(a+2)
C-) (b+2) .(b+3)
D-) (y-2) . (y+5)

Answer 1

multiplique os termos usando a propriedade distributiva o resultado vai ser
(x+3).(x+4)=x^2+4x+3x+12
assim vc pode fazer o resto sozinho é o mesmo principio 
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Answer 2

$A-) (x+3).(x+4)\\\\\\ x^{2} +4x+3x+12=0\to \\\\ x^{2} +7x+12=0\\\\ a=1; b=7; c=12\\\\ \Delta=b^2-4ac\to \Delta=7^2-4*1*12\to \Delta=49-48\to \Delta=1\\\\ x' \neq x''\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-7\pm \sqrt{1} }{2*1} \to x= \frac{-7\pm1}{2} \to \\\\ x'= \frac{-7+1}{2} \to x'= \frac{-6}{2} \to x'=-3\\\\ x''= \frac{-7-1}{2} \to x''= \frac{-8}{2} \to x''=-4\\\\\\ S=(-4;-3)$






$B-) (a+1).(a+2)\\\\\\a^2+2a+a+2=0\to \\\\ a^2+3a+2=0 \\\\ a=1;b=3;c=2\\\\ \Delta=b^2-4ac\to \Delta=3^2-4*1*2\to \Delta=9-8\to \Delta=1\\\\ a' \neq a''\\\\ a= \frac{-b\pm \sqrt{\Delta} }{2a} \to a= \frac{-3\pm \sqrt{1} }{2*1} \to a= \frac{-3\pm1}{2} \to \\\\ a'= \frac{-3+1}{2} \to a'= \frac{-2}{2} \to a'=-1\\\\ a''= \frac{-3-1}{2} \to a''= \frac{-4}{2} \to a''=-2\\\\ \\ S=(-2;-1)$






$C-) (b+2) .(b+3)\\\\\\ b^2+3b+2b+6=0\to \\\\ b^2+5b+6=0\to \\\\ a=1;b=5;c=6\\\\ \Delta=b^2-4ac\to \Delta=5^2-4*1*6\to \Delta=25-24\to \Delta=1\\\\ b' \neq b''\\\\ b= \frac{-b\pm \sqrt{\Delta} }{2a} \to b= \frac{-5\pm \sqrt{1} }{2*1} \to b= \frac{-5\pm1}{2} \to \\\\ b'= \frac{-5+1}{2} \to b'= \frac{-4}{2} \to b'=-2\\\\ b''= \frac{-5-1}{2} \to b''= \frac{-6}{2} \to b''=-3\\\\\\ S=(-3;-2)$






$D-) (y-2) . (y+5)\\\\\\ y^2+5y-2y-10=0\to \\\\y^2+3y-10=0\\\\ a=1;b=3;c=-10\\\\ \Delta=b^2-4ac\to \Delta=3^2-4*1*(-10)\to \Delta=9+40\to \Delta=49\\\\ y' \neq y''\\\\ y= \frac{-b\pm \sqrt{\Delta} }{2a} \to y= \frac{-3\pm \sqrt{49} }{2*1} \to y= \frac{-3\pm7}{2} \to \\\\y'= \frac{-3+7}{2} \to y'= \frac{4}{2} \to y'=2\\\\ y''= \frac{-3-7}{2} \to y''= \frac{-107}{2} \to y''=-5\\\\\\ S=(-5;2)$



Prontinho, espero ter ajudado...